Problem: Simplify the following expression: $z = \dfrac{2r + 3}{4} \div \dfrac{10r}{9}$
Explanation: Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{2r + 3}{4} \times \dfrac{9}{10r}$ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ (2r + 3) \times 9 } { 4 \times 10r}$ $z = \dfrac{18r + 27}{40r}$